He confesses that even though his Method “does not furnish an actual demonstration” of the results he’s interested in, it helps him figure out what’s true. It gives him intuition. As he says, “It is easier to supply the proof when we have previously acquired, by the method, some knowledge of the questions than it is to find it without any previous knowledge.” In other words, by noodling around, playing with the Method, he gets a feel for the territory. And that guides him to a watertight proof. This is such an honest account of what it’s like to do creative mathematics. Mathematicians don’t
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